Americans overwhelmingly support the diplomatic agreement between the United States and Russia to eliminate Syria’s chemical weapons, despite having deep doubts about the Syrian regime’s compliance and giving low marks overall for how President Obama is handling the situation, according to a new Washington Post-ABC News poll.

The president faced strong public opposition when he initially argued for military strikes against the Syrian regime in retaliation for its alleged use of chemical weapons. That opposition is largely unchanged in the new survey, with 61 percent saying that they are against such strikes.

But if Syria balks at the terms of the agreement, Obama could face reduced resistance to the use of military power to enforce the pact. Asked whether they would favor a congressional resolution authorizing force if the deal does not yield results, 44 percent say they would support it and 48 percent say they would not.

The president and other administration officials have said that the threat of military action was instrumental in bringing about the weekend agreement, which requires that Syria’s chemical weapons stocks be given up and eventually destroyed. The poll finds that 47 percent think the threat helped pressure Syria into agreeing to cede control of its chemical weapons, while 40 percent say the threat hurt diplomacy.

Obama drew more positive than negative reactions for last week’s nationally televised speech on Syria, with nearly half the country (47 percent) saying that he made a persuasive case for military action and about a third finding him unpersuasive. Notably, those who found him persuasive are twice as likely to say that the threat of military action helped force a diplomatic solution than hurt the situation.

Still, just 36 percent say they approve of his handling of the Syria situation, while 53 percent disapprove. Sixty percent of Democrats rate the president positively, while 79 percent of Republicans and 59 percent of independents rate him negatively.

Obama’s overall approval rating shows the country evenly divided, with 47 percent positive and 47 percent negative. That split represents a small but steady deterioration in his approval numbers since he was sworn in for a second term in January. His approval rating on international affairs is also 47 percent.

The path to the Syria deal was anything but direct, as the president first appeared ready to launch military strikes, then announced that he would seek congressional authorization, then seized on the diplomatic opening with the Russians that arose after what seemed to be an offhand comment by Secretary of State John F. Kerry.

Obama said in an interview with ABC’s George Stephanopoulos that aired Sunday that he is not concerned about criticism of the way he got to the deal, dismissing complaints about him and his administration as an excessive focus on style over results.

The Post-ABC poll was conducted as the fast-moving events were playing out. Interviews began Thursday, two days after Obama addressed the nation and just as the diplomatic negotiations in Geneva were beginning. The poll concluded Sunday, a day after the announcement that an agreement on Syria’s chemical weapons had been reached.

Americans responded positively to the diplomatic solution. About four in five say they back the initiative, though two in three say they are not confident that Syria will give up all its chemical weapons.

As he tried to make the case for military action, Obama faced heavy going and sought to assure people that military action would not lead to deeper involvement in Syria’s war. After a decade of war in Iraq and Afghanistan, the public is wary of another U.S. military engagement.

In the poll, 45 percent say U.S. vital interests are at stake in the Syrian conflict, while 48 percent say they are not. Around the time the United States invaded Iraq, about two-thirds said vital U.S. interests were involved.

Public opinion on this question appears closer to what it was when President Bill Clinton launched military strikes in Kosovo in 1999, though it is greater than during the Bosnia situation four years earlier.

The Syria issue has triggered discussion about the role of Russia and President Vladimir Putin and whether the unfolding events have strengthened Russia’s hand in the Middle East as the most powerful backer of Syrian President Bashar al-Assad.

Support for a??? Russian-proposed plan comes despite Americans’ broad distrust of the nation. In a separate poll released Monday by the Pew Research Center, two-thirds said the United States can trust Russia “not too much” or “not at all,” marking a slight increase from last year.

More broadly, the Post-ABC survey asked whether Obama’s handling of the Syria situation has put the United States in a stronger or weaker position in the world. On that question, 46 percent say it has not made much difference. Among those who think it has made a difference, more say it has weakened than say it has strengthened the U.S. position — 32 percent to 17 percent.

Despite Obama’s relatively weak ratings on his handling of the situation in Syria, he holds a clear advantage over Republicans in Congress in regard to whom people trust more on the issue, by 42 percent to 34 percent.

Fifty-four percent of Americans consider Obama a strong leader, compared with 61 percent a week before his second inauguration.

On other attributes, assessments of the president are not significantly different from previous Post-ABC polls. Americans split about evenly on the question of whether Obama shares their values, reflecting the partisan divisions in the country. Just over eight in 10 Democrats say he does, while nearly nine in 10 Republicans and a majority of independents say he does not.

Six in 10 Americans say Obama sticks to his principles. Republicans and Democrats are on opposite sides on this question, while a majority of independents say they think he does.

A bare majority says Obama is a good commander in chief. This question also produced a sharp partisan division, with Democrats overwhelmingly positive, Republicans overwhelmingly negative and independents closely split but with 50 percent saying yes.

The Post-ABC poll was conducted by telephone Thursday-Sunday among a random national sample of 1,004 adults, including interviews with land-line and cellphone-only respondents. The overall results have a margin of error of four percentage points.